Book reviews -- Numerical Recipes in Fortran by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery / Numerical Recipes Example Book (Fortran) by William T. Vetterling, Saul A. Teukalsky, William H. Press and Brian P. Flannery

Human Biology, Apr 1994 by Konigsberg, Lyle W

Numerical Recipes in Fortran: The Art of Scientific Computing, 2d edition, by William W. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. New York: Cambridge University Press, 1992. 963 pp. $49.95 (cloth).

Numerical Recipes Example Book (Fortran), 2d edition, by William T. Vetterling, Saul A. Teukolsky, William H. Press, and Brian P. Flannery. New York: Cambridge University Press, 1992. 245 pp. $29.95 (paper).

When the first edition of Press et al.'s Numerical Recipes was published in 1986, the book was immediately received as manna in the numerical wilderness. Only six years later, Press, Teukolsky, Vetterling, and Flannery have released the second edition of their landmark book. This of course raises the obvious question, If you already have the first edition, will you want or need the second? The answer is a definitive yes. The second edition of Numerical Recipes in Fortran is a book that should be on your desk (not your shelf) if you have any interests in the analysis of data or the formulation of models. The task of this review is not to convince the reader that this book (and the equivalent version for the C programming language) is superlative, because other reviews elsewhere will certainly trumpet the many virtues of this book. Instead, the focus here is on pointing out why Numerical Recipes is essential for the practicing human biologist or bioanthropologist.

First, is this book really a substantial revision of the 1986 edition? The answer here is that the second edition goes well beyond being a mere revision of the first edition. The second edition contains numerous additions of important material, such as a section on Cholesky decomposition (which is critical for simulating multivariate distributions), discussion of the bootstrap method, and the addition and expansion of other numerical methods too numerous to mention here. The book is organized into twenty chapters, which can be read more or less independently.

Second, is this a readable book? Certainly a book on numerical methods is not likely to make good bedtime reading; but the authors' style and presentation do make this an accessible volume. As in the first edition, they maintain an easy charm and wit throughout their discussions of what would on the surface appear to be rather dry topics. For example, in the introduction to the section on selection, Press et al. state, "Selection is sorting's austere sister (Say that five times quickly!)" (p. 333). In reference to the golden section search (a method for optimizing a function), they note that this procedure works "with the uncooperative minimum hunted down and cornered like a scared rabbit" (p. 395). In addition to these wry comments, another endearing feature of their style is that they do not shy away from making their opinions known. As a consequence, the reader can obtain useful advice from some of the leading scholars in the field of numerical analysis.

Finally, why do you need this book? In this age of increasing use of personal computers, there is plenty of numerical and statistical software available to the interested user. But the revolution in such software has largely come and gone, and we are left primarily with a set of useful packages for classical statistical analyses, most of which are firmly grounded in frequentist philosophies [see, for example, Press (1982) for a modern approach addressing both frequentist and Bayesian philosophies]. In addition to the rather classical nature of most personal computer statistical packages, it is ironic that the newer computer-intensive generation of statistical procedures [such as the bootstrap; see Diaconis and Efron (1983), Efron and Tibshirani (1991), and LePage and Billard (1992)] have not generally found their way into the personal computer mainstream. These newer techniques were largely developed to deal with small and difficult data sets, conditions that are often the norm in the study of human biology. For the moment, to incorporate newer statistical techniques, we need to write our own programs. Furthermore, it is doubtful that general personal computer programs will ever be able to keep pace with the rapid developments in statistical and numerical analysis while maintaining the generality that ensures that you can analyze everything of interest.

As an example of the need for writing one's own programs, consider the rapid developments in hazards analysis recently reviewed by Wood et al. (1992). Wood et al. (1992, p. 80) note that "many readily available statistical packages, such as SAS, SYSTAT, BMDP, GLIM, and SPSSX, now include modules for performing a wide variety of hazards analyses." In the earlier part of their text, though, Wood et al. (1992, pp. 48-49) present a likelihood equation and note that it can be maximized "numerically using a standard computer algorithm such as the Newton-Raphson, downhill simplex, or quasi-Newton method." They then note that "the useful series of books on Numerical Recipes provides computer code for all these algorithms." The bottom line, then, is if you have a typical problem in hazards analysis, you can turn to off-the-shelf computer packages; if your problem is not typical, you will need Numerical Recipes.